Congratulations, we have completed the first step to our induction proof! Next comes the *inductive step*, which begins with our definition of the induction hypothesis. The *induction hypothesis* supposes that our statement is true for some integer `k`

, with the caveat that `k`

must exceed the number set as the base case (Mazur 95).

Recall that we supposed that for any positive integer `n`

:

`$\sum^n_{i=1} (2i-1) = n^2$`

Using the definition of induction hypothesis as well as the fact that we defined the base case as `k = 1`

in the previous exercise, we can reword this conjecture to say this:
For some integer `k`

in which `k > 1`

:

`$\sum^k_{i=1} (2i-1) = k^2$`

We will use Python to code this hypothesis through the upcoming checkpoints. For convenience, we will set the variable `k`

equal to nine.

### Instructions

**1.**

First, create a variable called `s`

and set it equal to the default value of `0`

.

**2.**

Next, set `s`

to store the sum of first `i`

odd integers, where `i`

is a value starting at `1`

and increments each iteration until the first `k`

odd integers have been added together. In other words, rewrite:

`$\sum^k_{i=1} (2i-1)$`

using a Python script. Print `s`

to ensure that the code worked properly.

**3.**

Finally, use the `==`

comparison operator to write a Python script that prints whether or not `s`

really does equal `k**2`

.